Local Quadratic Approximation of 2D CG Vorticity Field and Extraction of Geometric Features

Abstract

In this paper, we propose a method of numerically approximating vorticity of simulated fluid and extracting their various geometrical characteristics. Our method uses quadratic forms in the approximation process, which can determine the structure of quadratic geometry of vorticity (ellipse, parabola, hyperbola). If the result is an ellipse, we can further extract useful geometrical information such as the center and major/minor axis length of an ellipse. We also investigate the relationship between these geometrical features and physical features of vorticity and show that an ellipse is near the center of the vortex while the parabola or hyperbola is highly related to the flow strain. Our method can be used to improve geometrical artifacts from existing fluid simulation methods such as vorticity confinement.